Final answer:
To graph the equation y = -1/4x + 2, start by plotting the y-intercept at (0, 2), then use the slope -1/4 to find another point by moving 4 units to the right and 1 unit down to (4, 1.5), and finally draw a straight line to connect these points.
Step-by-step explanation:
The question concerns the graphing of a linear equation, specifically y = -1/4x + 2. The y-intercept of a line is the point where it crosses the y-axis. For this equation, since there is no x value associated with the y-intercept and we have a constant value of 2, the y-intercept is (0, 2). To graph this line, one would first plot the y-intercept on the graph at the point (0, 2).
The slope, represented by 'm' in the slope-intercept form of a line (y = mx + b), in this case, is -1/4. This indicates that for every 4 units we move to the right along the x-axis (positive direction), the line will go down 1 unit on the y-axis (negative direction since the slope is negative). So starting at the y-intercept (0, 2), if we move 4 units to the right, we should move 1 unit down to determine the next point. Therefore, from the y-intercept, if we move 4 units right (which would get us to x = 4) we should move down 1 unit on the graph (which would get us to y = 1.5) and plot this point at (4, 1.5).
Finally, a straight line is drawn to connect these two points, extending it in both directions. We should draw this line straight since both the slope and y-intercept stay the same throughout the entire graph, creating a linear equation graph. The end result is a straight line that decreases from left to right, reflecting the negative slope.